Lesson with SimenN (Counterpoint, Analysis)

SimenN:

So, we have talked before and we did some small work concerning a brief look at Bach's first 2 part invention in C major, and we covered things like voice movement, but in order to have a proper start here, I'm going to direct our attention to Bach's Invention in D minor (Nr 4).

Before any analysis however, a little bit of guidance concerning what we'll be looking at and what the whole point of the analysis is:

The main point of Bach's inventions is to showcase fundamental techniques and forms which later he goes on to use in larger scale (Masses, etc). In essence, we'll be seeing how from a simple motive (melody or theme, in this case) a lot of different musical elements can be crafted, modified and reused so as to provide depth and form.

Not only that, but a fundamental element of counterpoint of the instrumental nature such as this is that there is no real way to "teach it" directly, as it is less a formula and more a certain handwork that must be acquired through practice and dedication.

The reason why we will be looking at instrumental counterpoint first and not functional harmony is due to your interest in the Baroque aesthetic, and because you simply wish to write in this style. However, there are certain harmonic conceptions that we have to be familiarized with as well, even if the bulk of the work is more to do with counterpoint.

In other words, the inventions are also a good way to get an idea of harmony, by virtue of their cleanness and form (which is dependent on tonality principles.)

So, with all this in mind, any questions?

If not, we can proceed to get our proverbial hands dirty!

Yepp SSC, Im starting right away!

Alrighty.

So, get your score ready, we'll be looking at the first page for now.

As far as scores, I'm using a Wiener Urtext Edition from Schott/Universal, UT 50042, with foot notes/analysis/sources from Ratz/F

Before continuing with the analysis, I would like to point out that for the purpose of developing the handwork necessary to properly get the "swing" of counterpoint, specially Bach's, I asked SimenN to copy inventions 1 and 4.

Copy, as in literally making a copy note for note, as was done in Bach's time. It is well known that was a practiced method by Bach himself to learn other composer's styles and it's extremely effective at developing a kind of muscle-memory for the nuances that can't be exactly explained or fitted into an automatic model or formula.

This was not only the case for Bach, but other composers such as Mozart, Schubert, Hindemith, all at some point took things from the past such as Baroque forms or idioms and tried their hand at it. Mozart himself late in his life had started to write a suite in baroque style (IE: Bach's french suites as model) which was very old-fashioned at his time. It was never finished, but fragments remain such as the Gigue in G major (KV 574).

Like Mozart, Bach himself had also experimented with old forms later in his life. Art of the fugue and the musical offering have a lot of very old concepts, such as a loose handling of Fugues, with things such as real answers despite subjects beginning at the 5th, and so on.

What all of these composers that took things from the past have in common, is that in doing so they were attempting also to get out new uses, inspiration, or seeing where they could take it. Luciano Berio's Sequenzas are based on ancient principles of church music (the name Sequenza itself comes from such practice, and Berio's father was a church musician himself), despite the fact the pieces themselves are a wonderful example of the 60s' "new music" modernism.

One doesn't need to look very far to find this phenomenon happening all over the 20th century as well. John Cage himself in his Sonatas for prepared piano falls back to the ancient concept of "sonatas", rather than the classical or romantic meaning. To Cage, as well as to pre-baroque and early baroque composers, a sonata stood on it's name as a moment of "Sound", hence the word "sonata" which comes from the word "sound."

In all instances, from Bach to Schnittke, the revival of the past always had the intention to try to find out where to actually go in the future. Mozart is a clear example of how his late works (like the mentioned suite fragments) work towards a tendency that only began to manifest itself clearly by the romantic period, years after his death despite the tendency to use it together with old styles and stylistic parameters.

So, the teaching of old disciplines must never be treated as a monolith of any sorts, but rather as means to really find out what these tools can bring a composer in terms of inspiration, perspective and understanding. Just like Mozart found the abandoned manuscripts in Leipzig laying still on the same place Bach had left them at St. Thomas church, sometimes rediscovering the past can mean a lot more than simply reliving it.

But all this as an aside, next post I'll continue with the invention as planned.

- Inversion: This means that all the interval relations are inverted, such as that a step up becomes a step down, an upwards jump becomes a downwards jump, and so on.

- Retrograded: This means that the subject is played "backwards", as if reading from back to front.

- Inversion + Retrograde: It's the combination of the above techniques.

- Augmentation: Means that a specific motive is changed in duration, by virtue of making each note a degree above in length. For example, a motive in 8ths is changed from 8ths to 4ths.

- Diminution: The opposite of augmentation, the length of a motive is reduced by virtue of reducing the length of each note a notch. For example, a motive in 4ths is changed from 4ths to 8ths.

Yess, i will try this out just to see if i have understod the explenation right!

score : [ATTACH]11786[/ATTACH]

Yes, that's how it is. There are more types of variations, but they all fall in one way or another in either of the already mentioned or a combination of them.

Alright, back to the analysis finally.

Last we left off, we were looking at the invention No.4 subject and techniques generally used to develop/variate/mess with themes, motives and subjects.

What I was talking about earlier, with the dissection of the subject into sections, plays a huge role in this Invention as well as others. Let's do quick overall look at how Bach writes the voices altogether, not looking directly at the counterpoint for now.

If you notice, the entire invention is built out of motives found on the first 2 measures (the subject). The scale movement, the jumps, and variations thereof make the entire melodic structure of the invention.

"But wait a minute, what about the 8ths in measure 3, right hand? How does the subject motives cover this?" Simple answer, they don't. The 8th figure here is a result of a baroque stylistic, which dictates that you should generally have note-duration contrasts. If you notice, most of the bulk of the invention is designed with 8ths vs 16ths except for a couple of sections.

And how did Bach come to the notes he uses in the 8ths sections such as in measure 3? One answer is that he arrived at it through harmonic principles. After all, measure 3 and 4 also mimic the dominant-tonic model from the subject. The first 8th group (measure 3) is a clear D minor chord, and the second is a dominant 7th (A major + 7th.)

The other, is that he arrived at them not only by harmonic, but also by the counterpoint itself. Clearly, the reason he chose the intervals in such way is to ensure a proper counterpoint line and melody (Hence G C(sharp) E in measure 4.)

Another thing to note, is that Baroque pieces are symbol-heavy, and a baroque composer in the norm will never use more than one type of "affect" per piece. That is to say, the character of the piece will remain the same from start till end, despite whatever subsequent variations. This is complimented by certain motives and idioms which were common-practice in the period which meant certain things (such as the passus duriusculus which meant sadness, pain, and so on.) This is also why Baroque composers were so keen on using the same musical material over and over, as opposed to Mozart and onwards where from one section to another the piece can take an entirely different character (different motives, etc etc.) It's a way to keep the "feel" of the piece from going anywhere else than the intended "affect".

So, now that we've covered some of the ground structure regarding melodies and motive material, let's look a little at the harmony.

An invention, like Bach's fugues (before the late period,) the inventions are composed with a form that works by following a certain set of patterns, such as going through certain tonalities, modulations, and so on. These patterns are defined in harmonic terms, despite the fact that function harmony at Bach's time was extremely primitive, certain concepts did exist as we know them today, such as the Dominant and Tonic.

As a sidenote: If you're keen on history and want to learn a little more on the roots of the terms such as Dominant, tonic, etc, check out Jean-Philippe Rameau's "Trait

So, while we're on the topic of melodies and tonality, let's actually do an exercise.

There's something important you have to understand before anything else, and that is that the less voices you have, the harder it is to imply a certain harmony. Surely, if you have broken chords on a single voice it's evident but otherwise you can blur the harmony to the point where it's really hard to tell what is what.

Counterpoint itself, as mentioned (and evidenced) in the analysis of Bach's invention above has harmony elements which give shape to the pieces and give them a form. However, the abstract nature of the technique itself can mean that harmony becomes very complicated to determine, or uncertain. So, for now let's not worry about actual harmony directly.

The exercise consists of writing 5 subjects for an invention such as the one analyzed. Something not longer than 2 measures, in simple rhythm (4/4, 3/4, etc). We'll work a little on expositions and instrumental counterpoint, but first you need to develop a sense of what feels "in style." It doesn't matter in what keys, tonalities or registers the subjects are, so long as they conform to what we saw in the invention, without directly copying it.

Yes, i have been away this weekend, ill be home later tonight! I will write some subjects! Thank you :) I have some questions to, i will ask you later

I composed some themes, I made them a little longer, there you can correct my errors to!

C Major Theme:

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[ATTACH]11885[/ATTACH]

A Minor Theme:

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G Major Theme:

[ATTACH]11888[/ATTACH]

[ATTACH]11889[/ATTACH]

E Minor Theme:

[ATTACH]11890[/ATTACH]

[ATTACH]11891[/ATTACH]

Well, let's see now. It does seem like you went a little overboard with the exercise in question, but nevermind that, let's see what you did.

The first subject in C major is pretty good. I like that you paid attention to the phrasing and articulation. There's not much else to say about it, it ends in the tonic and has a pretty obvious harmonic implications.

The second is... well. I see you tried to do a little development there, but the subject is a little too complex for what we need. It would be better suited for a fugue (It's a modulating subject, ending in the dominant as a modulation, rather than the 5th of the tonic.) The problem is also that you didn't really answer it like an invention, you answered it at the 5th (E minor) despite that inventions are answered at the octave. Not only that, but in the norm you never have the second voice start with anything other than a strict exposition of the subject. So, those two 8ths would be out of place in measure 2.

Obviously you have an idea of how it should look like, but the devil is in the details.

By the 3rd exercise you didn't really write a subject for an invention, it's just a 2 voice counterpoint which could as well be part of a prelude, and actually sounds like a particular prelude out of the well tempered klavier (let's see if you can see which!) It's pretty, sure, but it's not what I asked for. I know you're eager to actually do stuff and write, but, if we don't focus on specific things first it won't help you in the long run.

The 4th exercise has a really good subject, though the counterpoint was weird and again you didn't answer it at the octave, so it seems like a half-baked fugue exposition. We'll get to fugues after you show a good grasp on the simpler Invention/canon/etc forms, since Fugues depend on the same principles as these other forms and they are easier to study than fugues because they are more strict*.

Let's take the first subject you wrote in C major and actually build up an invention, but without actually writing a single note yet. From the analysis of Bach's (Nr.1 and Nr.4) what do you think the structure will be?

*Indeed, Fugues are very free in terms of structure as a fugue in itself is not a song form, it's simply a type of counterpoint technique. After the exposition you are free to do almost whatever you want, and indeed Bach's fugues are EXTREMELY diverse in structure, character, techniques, etc etc. So, instead, it's better to learn the techniques where the forms are simpler and more strictly structured.

Well, I belive the structure would be something like the 1 invention by Bach, i think the theme fits the first structure, is that right?

Well, I belive the structure would be something like the 1 invention by Bach, i think the theme fits the first structure, is that right?

What does this mean exactly? Do you want to give a shot at sketching out an actual structure based on the invention? Don't write anything, just let's actually have it in theory here before anyone writes any music.

I'll give you some pointers;

The best way to get a simple structure done like this is to set some checkpoints.

So, we know that pretty much all baroque pieces have to modulate at some point or another to the dominant, so that's our first stop. Then, it's usual that they modulate to the relative major/minor/so on, so that if the piece is in major, that section is in minor. And usually, after this, it modulated back to the tonic and ends (unless it's something loooooong, which we aren't going to deal with yet.)

So, in C major, you'd need to pass through G major, A minor, and then back to C major in theory.

If you're thinking in harmony terms, we have the keys we need already, but there's the question of how and when. The usual way for Baroque composers to modulate is through sequences, so use sequences to modulate into these keys.

To establish that you're in the key that you want to modulate to, you only need to pass through the 7th degree (of the new key. IE: in G major, F sharp.) while moving upwards (leading note) a couple of times, if you don't want to do a cadence proper. It is usually so that this is followed by an exposition of the subject in the new key.

Functionally, think of trying to have the dominant of the key you're going to right before it's introduction, without actually spelling the chord out, just important notes. If you're going to G major, for example, you should probably have an F sharp (leading note!) somewhere around to signal the new key as F sharp is the 3rd from D major (the dominant from G major.) So you would have a simple Dominant -> Tonic in the new key.

You don't need to spell out the chords, like I said, you can simply pick out which notes are important such as the leading note, and integrate it into the modulating sequence.

Let's practice this idea some. Can you write the invention using the subject we agreed on up until the modulation to G major? (Stop once the subject enters in G major.)

I'm sure you can, so do it. As usual, if you have any questions, just shoot.

Yepp ill do it now

I did some invention like sinfonia stuff, I know I use to many themes, that is why the sinfonia like! :)

[ATTACH]11968[/ATTACH]

[ATTACH]11969[/ATTACH]

Alright, I see you did a good job following the structure that I gave you. You modulated to and from the keys pretty cleanly for MOST part, but the counterpoint here needs a lot of work.

First of all, an invention has an exposition like a fugue, or an imitation to be precise. You need the one voice exposition at the start so that the subject is burned into the listener's brain. If you start out with a counterpoint as well it's unclear what should be recognizable/characteristic.

Second, remember to check your counterpoint for parallels. No to only you had some pretty nasty 8th parallels in measure 7, but that jump to F sharp in the right hand is totally unnecessary. You could've gone from B to D and descended in 6ths. Measures 7 and 8 are only parallels, which isn't good at all in 2 voice counterpoint unless you were going for something modern/non traditional, etc.

Third, let's look a little at how leading notes work. A leading note, in this case the F sharp that first shows up in measure 6, must resolve to G so that the key of G is established. You have to be careful at how you approach them, or you can risk a rather sudden/jarring tonality shift (such as what you did in measure 7.) To correct that specific area, follow what I said and instead of jumping from B to F sharp, jump from B to D. The idea is that leading notes have to be somewhat avoided since their harmonization and counterpoint instantly moves you closer to the dominant/cadence build unless they're a passing note. In other words, a leading note in a strong beat generally implies you'll be heading into a cadence.

Fourth, you also modulated right into D major, which is the double dominant from C which is where you start. Technically, you still go to G major afterwards, but it's not typical to go to too far away in the circle of 5ths before the modulation to the dominant key. The modulation to A minor is pretty well done, you move upwards in a sequence and slip in the G sharp, which move upwards to A and the key change is more or less established.

Fifth, while you got some pretty good sequences going, there are areas which sound more reminiscent from Mozart/Vienna Classic than baroque composers. For example measure 33, with the tone repetitions.

I'm not sure if you know about baroque "affects" and the aesthetic for baroque music. A baroque piece must only have a single "affect." That is, the character of the piece must always be the same and it can only have one character. This is crucial in understanding why baroque music has such a big emphasis on motive unity and economy of themes/motives. You need to work with only what you give at the start, what sets "The affect" or "character" of the piece, so that the character is not compromised.

Your motive there with the repetitions is an entirely different affect, has a different character than the motives you've been using up to that point. Indeed, the tone repetition is a specific baroque motive which is also tied to different traditions, etc etc, than other motives.

The moment where the baroque "affect" stuff starts going out the window is precisely with CPE Bach and the Vienna Classic, where there's a huge emphasis on motive contrasts in a very short space of time. You can have by Mozart one measure with X and Y motives, and the next Z and X plus different rhythms. This isn't so in the baroque aesthetic conception.

Sixth, ornamentations don't just go "whenever you want." In harpsichord, ornamentations are usually added where the composer would have otherwise added a strong dynamic marking, or to signal an important moment in the piece. For example, it's not unusual to see the leading note in a 4-3 suspension cadence in a baroque piece with a triller or mordent. This is because the leading note can be easily emphasized so the cadence is made more robust or clearer. Plus, a baroque player would add their own ornamentations on top of the written ones depending on their interpretation so don't write too many of them.

So now, after this long list of stuff, can you actually do what I asked you to? ;P

Write a again an invention, with the same subject, in C major, but like a correct invention. Minding that your counterpoint is 8th-5th parallel free, using motive conservation and trying to keep the same "character" throughout the piece. Start only with one voice, with the subject exposition and then add the second voice at the octave in the other hand, developing from there.

Sinfonias are slightly different and more complex, so we'll be looking at them after I see that you've gotten all this stuff about inventions down.

Thanks i have some questions :

Leading Notes:

The F# in ms. 6, goes G F# D , and next ms. its starts on G. how does it work? it the rule F# have to end at G, or can i do what i did with the F# and D, both are part of the dominant and they end up in G major, but is it allowed?

The Octaves, hehe yes, it seems i typed the worng notes, should be in thirds.

What is a pasing note?

Yepp I will give it a shot, just develope the theme then, but i tire of that theme, ill make a new one is that oki?

Thanks i have some questions :

Leading Notes:

The F# in ms. 6, goes G F# D , and next ms. its starts on G. how does it work? it the rule F# have to end at G, or can i do what i did with the F# and D, both are part of the dominant and they end up in G major, but is it allowed?

The Octaves, hehe yes, it seems i typed the worng notes, should be in thirds.

What is a pasing note?

Yepp I will give it a shot, just develope the theme then, but i tire of that theme, ill make a new one is that oki?

Well sure, make a new subject if you want. But keep it short and simple, please.

As for the questions, yeah, what's in measure 6 is OK, because the F sharp is a passing note. A passing note means that it's a note between two others like the F sharp here. It's not on an accentuated beat, and it's usually approached/moving in step-motion (rather than jumps.)

It would've been wiser to do a small cadence (f sharp -> g) after the introduction of the F sharp, rather than continuing on to D major. In other words, you should've done "G, F sharp, G" rather than "G, F sharp, E."

Though F sharp and D are part of G major, the interval relation of F sharp and D is dominant (in G major) so you want to avoid that precise interval UNLESS you plan to use it as a cadence to G major (IE, F sharp moves to G.)

That's the fundamental problem with that small passage, I hope it's clearer now.

Not to nag, but are you still interested in going on with this? Just asking, so the thread doesn't go into oblivion.

yess i am :D what to do next?

WELL!

How about we work on the invention I asked you to do? ;P

Additionally, if you want I can look at other stuff you've done here so long as they're related to our current study of counterpoint and so on, yea?

yes please take a look at the other stuff i have done, like the piano preludes and flute suite! ill work on an invention tomorrow!

i did a invention like : please correct :D

Midi:

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Score:

[ATTACH]13072[/ATTACH]